#### Answer

The ball's rebound velocity is 6.0 m/s

#### Work Step by Step

We can use the graph to find the impulse exerted on the ball. The impulse is equal to the area under the force versus time graph.
$J = ~F_x~t$
$J = (500~N)(8.0\times 10^{-3}~s)$
$J = 4.0~N~s$
We can use the impulse to find the final momentum $p_f$.
$p_f = p_0+J$
$p_f = m~v_0+J$
$p_f = (0.25~kg)(-10~m/s)+4.0~N~s$
$p_f = 1.5~N~s$
We can use the final momentum to find the rebound velocity $v_{fx}$.
$m~v_{fx} = p_f$
$v_{fx} = \frac{p_f}{m}$
$v_{fx} = \frac{1.5~N~s}{0.25~kg}$
$v_{fx} = 6.0~m/s$
The ball's rebound velocity is 6.0 m/s.